Documents published in Scipedia

• Linear and quadratic invariants preserving discretization of Euler equations

  G. Coppola, A. Veldman

  eccomas2022.

  
  

  Abstract

  In the context of the numerical treatment of convective terms in compressible transport equations, general criteria for linear and quadratic invariants preservation, valid on uniform and non-uniform (Cartesian) meshes, have been recently derived by using a matrix-vector approach, for both finite-difference and finite-volume methods ([1, 2]). In this work, which constitutes a follow-up investigation of the analysis presented in [1, 2], this theory is applied to the spatial discretization of convective terms for the system of Euler equations. A classical formulation already presented in the literature is investigated and reformulated within the matrix-vector approach. The relations among the discrete versions of the various terms in the Euler equations are analyzed and the additional degrees of freedom identified by the proposed theory are investigated. Numerical simulations on a classical test case are used to validate the theory and to assess the effectiveness of the various formulations.

  Abstract
  In the context of the numerical treatment of convective terms in compressible transport equations, general criteria for linear and quadratic invariants preservation, valid [...]

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• Validation on a new anisotropic four-parameter turbulence model for low Prandtl number fluids

  L. Sirotti, G. Barbi, A. Chierici, V. Giovacchini, S. Manservisi

  eccomas2022.

  
  

  Abstract

  This work aims to validate a new anisotropic four-parameter turbulence model for low-Prandtl number fluids in forced and mixed convection. Traditional models based on the gradient-diffusion hypothesis and Reynolds analogy are inadequate to simulate the turbulent heat transfer in low-Prandtl number fluids. Additional transport equations for thermal variables are required to predict the characteristic thermal time scale. In a four-parameter turbulence model, two additional transport equations are solved for the temperature variance and its dissipation rate. Thus, it is possible to formulate appropriate characteristic time scales to predict the near-wall and bulk behaviour of mean and turbulent variables. The isotropic version of the four-parameter model has been widely studied and validated in forced and mixed convection. We aim to extend the model validity by proposing explicit algebraic models for the closure of Reynolds stress tensor and turbulent heat flux. For the validation of the anisotropic four-parameter turbulence model, low-Prandtl number fluids are simulated in several flow configurations considering buoyancy effects and numerical results are compared with DNS data.

  Abstract
  This work aims to validate a new anisotropic four-parameter turbulence model for low-Prandtl number fluids in forced and mixed convection. Traditional models based on the [...]

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• Numerical Testcases to Study Proudman Resonance Using Shallow Water Models

  N. Beisiegel, J. Behrens

  eccomas2022.

  
  

  Abstract

  Proudman resonance is the dominant mechanism behind meteotsunamis. We develop a comprehensive set of testcases to validate numerical methods focusing on the performance with respect to represent mentioned resonance. With the test cases we assess the wave amplification in dependence of characteristics of the pressure perturbation, model parameters, model resolution, and bathymetry characteristics. We use the compilation of tests to validate an adaptive discontinuous Galerkin (DG) model for the two-dimensional non-linear shallow water equations. As the tests are highly sensitive to model resolution, we use the adaptive mesh capabilities of the model to locally refine the disturbance and thus gain considerable efficiency.

  Abstract
  Proudman resonance is the dominant mechanism behind meteotsunamis. We develop a comprehensive set of testcases to validate numerical methods focusing on the performance with [...]

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• Correcting the discretization error of coarse grid CFD simulations with machine learning

  A. Kiener, S. Langer, P. Bekemeyer

  eccomas2022.

  
  

  Abstract

  Computational fluid dynamics is a cornerstone for the modern aerospace industry, providing important insights on aerodynamic analysis while reducing the need of expensive experiments and tests. Nevertheless, simulations of complex geometries are often performed on a discrete spatial domain too coarse to capture all relevant physical phenomena for the sake of lowering the computational cost. A consistent spatial discretization on so-called grids approximates the analytical solution of the partial differential equation with increasing number of discrete points. Such a grid refinement study is an expensive method to assess the general grid quality. This work shows that machine learning as a post-processing tool is capable of improving coarse grid simulations, even if not converged. The results show that three machine learning models varying in their complexity, namely the random forest, the neural network, and the graph neural network, are capable of finding patterns in coarse grid simulations. These patterns are used to predict the discretization error to approximate the field variables of interest of the corresponding fine grid simulation mapped onto the coarse grid. Initial training and testing is performed on the RAE2822 airfoil leading to corrected flow fields, improved surface integrals and coefficients, even when shocks are present. Additional tests are performed on the RAE5212 airfoil, showing the generalization limits of the trained models. The proposed method promises to reduce computational expenses while increasing the accuracy of the coarse grid results which works locally, e.g. it corrects the error for each cell individually and is therefore not restricted by the number of grid points. The presented results obtained by the machine learning models during post-processing are a promising baseline for more integrated developments, where the models will interact in a dynamic fashion with the flow solver to further improve coarse grid simulations.

  Abstract
  Computational fluid dynamics is a cornerstone for the modern aerospace industry, providing important insights on aerodynamic analysis while reducing the need of expensive [...]

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• SPDE-ConvNet: Predict stabilization parameter for Singularly Perturbed Partial Differential Equation

  S. Yadav, S. Ganesan

  eccomas2022.

  
  

  Abstract

  Singularly Perturbed Partial Differential Equations are challenging to solve with conventional numerical techniques such as Finite Element Methods due to the presence of boundary and interior layers. Often the standard numerical solution has spurious oscillations in the vicinity of these layers. Stabilization techniques are employed to eliminate these spurious oscillations in the numerical solution. The accuracy of the stabilization technique depends on a user-chosen stabilization parameter, where an optimal value is challenging to find. In this work, we focus on predicting an optimal value of the stabilization parameter for a stabilization technique called the Streamline Upwind Petrov Galerkin technique for solving singularly perturbed partial differential equations. This paper proposes SPDE-ConvNet, a convolutional neural network for predicting stabilization parameters by minimizing a loss based on the cross-wind derivative term. The proposed technique is compared with the state-of-the-art variational form-based neural network schemes.

  Abstract
  Singularly Perturbed Partial Differential Equations are challenging to solve with conventional numerical techniques such as Finite Element Methods due to the presence of boundary [...]

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• Simulation of massively separated flows and rotating machine flows using hybrid models

  F. Miralles, B. Sauvage, A. Duben, V. Bobkov, T. Kozubskaya, S. Wornom, B. Koobus, A. Dervieux

  eccomas2022.

  
  

  Abstract

  RANS, DES, hybrid RANS/DVMS and DDES/DVMS models are introduced in low dissipation schemes. They are compared for the simulation of vortex shedding flows around a NACA0021 at high angle of attack and a Caradonna-Tung helix.

  Abstract
  RANS, DES, hybrid RANS/DVMS and DDES/DVMS models are introduced in low dissipation schemes. They are compared for the simulation of vortex shedding flows around a NACA0021 [...]

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• Matrix properties associated with discrete conservation in flow simulations

  A. Veldman, G. Coppola

  eccomas2022.

  
  

  Abstract

  Supraconservative discretization methods are studied which conserve primary (mass, momentum and internal energy) as well as secondary (total energy) invariants. In particular, the coefficient matrices which are related to such conservation properties are analyzed. This analysis holds for any discretization method with a volume-consistent scaling.

  Abstract
  Supraconservative discretization methods are studied which conserve primary (mass, momentum and internal energy) as well as secondary (total energy) invariants. In particular, [...]

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• Energy-preserving stable computations of high-pressure supercritical fluids turbulence

  M. Bernades, F. Capuano, F. Trias, L. Jofre

  eccomas2022.

  
  

  Abstract

  High-fidelity computations of turbulent flows at high-pressure supercritical fluid conditions present significant challenges. Besides the inherent broadband nature of the flow, the rapid variation of thermophysical properties across the pseudo-boiling region can result in additional complexities in terms of strong localized density gradients, spurious pressure oscillations, non-linear behaviour of fluids, and amplification of aliasing errors. Different research groups have utilized distinct approaches to achieve numerical stability, mostly resorting to upwindbiased schemes, artificial dissipation and/or high-order filtering. However, in these strategies, stability is achieved at the expense of artificially suppressing part of the turbulent energy spectrum. In this regard, this work aims to explore the suitability, in terms of stability and accuracy, of recently proposed energy-preserving schemes for scale-resolving simulations of supercritical turbulence. For ideal gases, such type of methods have been demonstrated to provide stable and accurate computations of turbulence by preserving kinetic energy and/or other quantities of physical relevance. However, their extension to real-gas thermodynamic frameworks is still in its infancy, and consequently requires to be carefully investigated. To this objective, this work analyzes the performance of different classical and energy-preserving discretizations under ideal-gas conditions, and carries out an initial assessment of their performance at high-pressure supercritical fluid regimes. The results obtained indicate that their extension to real-gas thermodynamics is not straightforward, and consequently motivate the necessity to develop new solutions able to satisfy the desired stability and accuracy requirements.

  Abstract
  High-fidelity computations of turbulent flows at high-pressure supercritical fluid conditions present significant challenges. Besides the inherent broadband nature of the [...]

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• A three-dimensional FVC scheme on non-uniform tetrahedron meshes: application to the 3D Euler equation

  M. Ziggaf, I. Kissami, M. Boubekeur, F. Benkhaldoun, I. El mahi

  eccomas2022.

  
  

  Abstract

  This study is about the construction of a numerical scheme of the predictor-corrector type in conservative form for solving general systems of conservation laws in multiple space dimensions on unstructured meshes. The work is a generalization of the one-dimensional finite volume characteristics (FVC) scheme and is related to the work of Fayssal Benkhaldoun and Mohammed Sead. The construction of the intermediate state is based on the method of characteristics, while the corrective stage recovers the conservation equations. The scheme is accurate to first order, monotonic and entropic; it avoids Riemann solvers at each interface; it also allows for improved accuracy order in time and space on unstructured three-dimensional meshes in the framework of the finite volume method. The scheme's performance is evaluated through a series of test benchmarks for the three-dimensional version of the Euler equations..

  Abstract
  This study is about the construction of a numerical scheme of the predictor-corrector type in conservative form for solving general systems of conservation laws in multiple [...]

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• CFD validation of a controllable pitch marine propeller using a truly autonomous mesh generation with adaptive mesh refinement

  M. Vångö, P. Scienza

  eccomas2022.

  
  

  Abstract

  The design of propellers for maritime propulsion systems has a long history of using Computational Fluid Dynamics (CFD) as result of the constant desire to improve efficiency. The complex physics in addition to the motion of the propellers pose several challenges to CFD investigations, in particular with regards to mesh generation. In view of addressing these challenges, the present work proposes an alternative approach, which employs an autonomous mesh generation based on a modified Cartesian cut-cell methodology with Adaptive Mesh Refinement (AMR). In this work, this approach is validated against the extensive open measurement data of the Potsdam Propeller Test Case (PPTC) from SVA Potsdam, which contains both open water tests as well as detailed transient velocity field measurements. Additionally, benefits of both steady-state and fully-moving transient approaches for propeller numerical analyses are discussed, together with a future outlook on cavitation phenomena within the presented framework.

  Abstract
  The design of propellers for maritime propulsion systems has a long history of using Computational Fluid Dynamics (CFD) as result of the constant desire to improve efficiency. [...]

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